Theory Of Non-equilibrium Thermodynamics Research Articles

Thermophoretic torque in colloidal particles with mass asymmetry.

We investigate the response of anisotropic colloids suspended in a fluid under a thermal field. Using nonequilibrium molecular dynamics computer simulations and nonequilibrium thermodynamics theory, we show that an anisotropic mass distribution inside the colloid rectifies the rotational Brownian motion and the colloids experience transient torques that orient the colloid along the direction of the thermal field. This physical effect gives rise to distinctive changes in the dependence of the Soret coefficient with colloid mass, which features a maximum, unlike the monotonic increase of the thermophoretic force with mass observed in homogeneous colloids.

A Morse index invariant reduction of non-equilibrium thermodynamics

We consider the finite dimensional reduction of the well known non-equilibrium thermodynamics theory developed through the last two decades by a team of researchers lead by Giovanni Jona-Lasinio, realized by considering a simplified version – a reaction-diffusion-like dynamics – of that theory. We begin with a clear axiomatic format of that framework, showing that the reaction-diffusion dynamics emerge in a direct way after a few assumptions. Our goal is to put focus on the relations between the reduced and the full theory and to underline some topological features of this theory, more precisely, by first showing that the Morse index distribution of the equilibria of the finite dimensional reduced system is exactly the same of the full original system, thus giving us eventually a good measure of the robustness of the reduction, and secondly, moving our framework to a Morse–Smale setting, by proposing an alternative way to compute the Morse index of the equilibria. In order to realize this last program, we propose a weak infinite-dimensional Maslov–Hörmander theorem.

Phase-field model for liquid–solid phase transition of physical hydrogel in an ionized environment subject to electro–chemo–thermo–mechanical coupled field

In this paper, a phase-field model is developed for simulation of the phase transition of physical hydrogels between the liquid solution and solid gel states in an ionized environment, subject to an externally applied electro-chemo-thermo-mechanical multiphysics coupled field. The presently developed model consists of the governing equations for the equilibrium of forces, the conservations of energy and mass, and the Maxwell's equations. Based on the second law of thermodynamics, the constitutive equations are formulated from the entropy viewpoint, including a novel Ginzburg–Landau type of free energy with the effect of crosslink density, which may be reduced to that for a chemical hydrogel if a constant crosslink density is considered. In order to identify the phases for the present domain covering the gel and solution states, the crosslink density is defined as a novel phase field in such a way that the solution phase is identified when the crosslink density is small, while the gel identified if the crosslink density becomes large, and an addition kinetic equation is imposed on the crosslink density as the phase field for phase transition. It is examined that the present model can be reduced to a published non-equilibrium thermodynamic theory, if the interface is ignored when only a single bulk phase exists, i.e. no phase transition occurs. Furthermore, the mechanical field formulated in the present paper is coupled with the thermal, electrical, and chemical multiphysics fields simultaneously, while the mechanical fields in the published works were coupled with either the thermal or electro–chemical field only. As a case study, the system at equilibrium state is investigated numerically to analyze the influences of the electrical and chemical potentials as well as mechanical pressure externally imposed on the boundary of the system domain. Another case study presents a spherically symmetrical liquid-solid phase transition at non-equilibrium states in an ionized environment, with the emphasis on the evolutions of the interface, crosslink density and chemical potentials.

Predictions of cyclic yielding behavior of solids based on a nonequilibrium thermodynamic theory

A nonequilibrium thermodynamic framework for solids is proposed in this study to account for and predict the fundamental mechanical behavior of stability and yielding in solid materials. The constitutive relations are derived from the nonequlibrium thermodynamic descriptions of the mechanical system of solids, including the elastic potential, the entropy production and the excess entropy production. Based on such an approach, the yielding behavior of solids can be well interpreted by the stability of thermodynamic steady state. Thus, employing the Lyapunov theory, a general yield criterion is proposed theoretically for solids based on the evolution direction of excess entropy, which depends on the excess entropy production defined. The yielding criteria of metals and granular solids are then specified and are shown to be efficient in predicting the isotropic and kinematic hardening behavior of solids. The kinematic hardening of yield loci is attributed to the residual stress induced by the irreversible deformation. As an important application of this theory, the cyclic behavior of solids under various cyclic loads can also be well predicted from the perspective of thermodynamics.

Thermodynamic Analysis of TEG-TEC Device Including Influence of Thomson Effect

AbstractA thermodynamic model of a thermoelectric cooler driven by thermoelectric generator (TEG-TEC) device is established considering Thomson effect. The performance is analyzed and optimized using numerical calculation based on non-equilibrium thermodynamic theory. The influence characteristics of Thomson effect on the optimal performance and variable selection are investigated by comparing the condition with and without Thomson effect. The results show that Thomson effect degrades the performance of TEG-TEC device, it decreases the cooling capacity by 27 %, decreases the coefficient of performance (COP) by 19 %, decreases the maximum cooling temperature difference by 11 % when the ratio of thermoelectric elements number is 0.6, the cold junction temperature of thermoelectric cooler (TEC) is 285 K and the hot junction temperature of thermoelectric generator (TEG) is 450 K. Thomson effect degrades the optimal performance of TEG-TEC device, it decreases the maximum cooling capacity by 28 % and decreases the maximum COP by 28 % under the same junction temperatures. Thomson effect narrows the optimal variable range and optimal working range. In the design of the devices, limited-number thermoelectric elements should be more allocated appropriately to TEG when consider Thomson effect. The results may provide some guidelines for the design of TEG-TEC devices.

Metal viscoplasticity with two-temperature thermodynamics and two dislocation densities

Posed within the two-temperature theory of non-equilibrium thermodynamics, we propose a model for thermoviscoplastic deformation in metals. We incorporate the dynamics of dislocation densities–mobile and forest—that play the role of internal state variables in the formulation. The description based on two temperatures appears naturally when one recognizes that the thermodynamic system undergoing viscoplastic deformation is composed of two weakly interacting subsystems, viz. a kinetic-vibrational subsystem of the vibrating atomic lattices and a configurational subsystem of the slower degrees of freedom relating to defect motion, each with its own temperature. Starting with a basic model that involves only homogeneous deformation, a three-dimensional model for inhomogeneous viscoplasticity applicable to finite deformation is charted out in an overstress driven viscoplastic deformation framework. The model shows how the coupled evolutions of mobile and forest dislocation densities, which are critically influenced by the dynamics of configurational temperature, govern the strength and ductility of the metal. Unlike most contemporary models, the current proposal also affords a prediction of certain finer details as observed in the experimental data on stress–strain behaviour of metals and this in turn enhances the understanding of the evolving and interacting dislocation densities.

Shooting and Arc-Length Continuation Method for Periodic Solution and Bifurcation of Nonlinear Oscillation of Viscoelastic Dielectric Elastomers

A majority of dielectric elastomers (DE) developed so far have more or less viscoelastic properties. Understanding the dynamic behaviors of DE is crucial for devices where inertial effects cannot be neglected. Through construction of a dissipation function, we applied the Lagrange's method and theory of nonequilibrium thermodynamics of DE and formulated a physics-based approach for dynamics of viscoelastic DE. We revisited the nonlinear oscillation of DE balloons and proposed a combined shooting and arc-length continuation method to solve the highly nonlinear equations. Both stable and unstable periodic solutions, along with bifurcation and jump phenomenon, were captured successfully when the excitation frequency was tuned over a wide range of variation. The calculated frequency–amplitude curve indicates existence of both harmonic and superharmonic resonances, soft-spring behavior, and hysteresis. The underlying physics and nonlinear dynamics of viscoelastic DE would aid the design and control of DE enabled soft machines.

Wax deposition rate model for heat and mass coupling of piped waxy crude oil based on non-equilibrium thermodynamics

ABSTRACTIn this paper, wax deposition in waxy crude oil transportation process was regarded as an irreversible process. Based on the entropy production rate equations, the linear phenomenological equations for the diffusion of wax molecules were derived by using the theory and method of non-equilibrium thermodynamics and heat-mass transfer. Combined with the mass and energy conservation laws, the differential equations of heat and mass transfer in the process of pipeline transportation were established, and the molecular diffusion rate of dissolved wax was solved. On the basis of this, the mathematical model of actual wax deposition rate was established by considering the attachment process and scouring process of the wax molecules. Taking an oil pipeline in Daqing as an example, the change law and influencing factors of the wax molecular diffusion coefficient, the wax deposition rate, and the net wax deposition rate were studied by numerical simulation. The wax deposition rate test results of the laboratory loop test were compared with the theoretical calculation results in order to analyze the accuracy and the adaptability of heat and mass coupling mechanism and to provide a theoretical basis for further study of wax deposition in the process of waxy oil pipeline transportation.

Nonequilibrium thermodynamics of the Markovian Mpemba effect and its inverse

Under certain conditions, it takes a shorter time to cool a hot system than to cool the same system initiated at a lower temperature. This phenomenon-the "Mpemba effect"-was first observed in water and has recently been reported in other systems. Whereas several detail-dependent explanations were suggested for some of these observations, no common underlying mechanism is known. Using the theoretical framework of nonequilibrium thermodynamics, we present a widely applicable mechanism for a similar effect, the Markovian Mpemba effect, derive a sufficient condition for its appearance, and demonstrate it explicitly in three paradigmatic systems: the Ising model, diffusion dynamics, and a three-state system. In addition, we predict an inverse Markovian Mpemba effect in heating: Under proper conditions, a cold system can heat up faster than the same system initiated at a higher temperature. We numerically demonstrate that this inverse effect is expected in a 1D antiferromagnet nearest-neighbors interacting Ising chain in the presence of an external magnetic field. Our results shed light on the mechanism behind anomalous heating and cooling and suggest that it should be possible to observe these in a variety of systems.

Steepest-entropy-ascent nonequilibrium quantum thermodynamic framework to model chemical reaction rates at an atomistic level.

The steepest entropy ascent (SEA) dynamical principle provides a general framework for modeling the dynamics of nonequilibrium (NE) phenomena at any level of description, including the atomistic one. It has recently been shown to provide a precise implementation and meaning to the maximum entropy production principle and to encompass many well-established theories of nonequilibrium thermodynamics into a single unifying geometrical framework. Its original formulation in the framework of quantum thermodynamics (QT) assumes the simplest and most natural Fisher-Rao metric to geometrize from a dynamical standpoint the manifold of density operators, which represent the thermodynamic NE states of the system. This simplest SEAQT formulation is used here to develop a general mathematical framework for modeling the NE time evolution of the quantum state of a chemically reactive mixture at an atomistic level. The method is illustrated for a simple two-reaction kinetic scheme of the overall reaction F+H_{2}⇔HF+F in an isolated tank of fixed volume. However, the general formalism is developed for a reactive system subject to multiple reaction mechanisms. To explicitly implement the SEAQT nonlinear law of evolution for the density operator, both the energy and the particle number eigenvalue problems are set up and solved analytically under the dilute gas approximation. The system-level energy and particle number eigenvalues and eigenstates are used in the SEAQT equation of motion to determine the time evolution of the density operator, thus effectively describing the overall kinetics of the reacting system as it relaxes toward stable chemical equilibrium. The predicted time evolution in the near-equilibrium limit is compared to the reaction rates given by a standard detailed kinetic model so as to extract the single time constant needed by the present SEA model.

A non-equilibrium thermodynamic model for tumor extracellular matrix with enzymatic degradation

The extracellular matrix (ECM) of a solid tumor not only affords scaffolding to support tumor architecture and integrity but also plays an essential role in tumor growth, invasion, metastasis, and therapeutics. In this paper, a non-equilibrium thermodynamic theory is established to study the chemo-mechanical behaviors of tumor ECM, which is modeled as a poroelastic polyelectrolyte consisting of a collagen network and proteoglycans. By using the principle of maximum energy dissipation rate, we deduce a set of governing equations for drug transport and mechanosensitive enzymatic degradation in ECM. The results reveal that osmosis is primarily responsible for the compression resistance of ECM. It is suggested that a well-designed ECM degradation can effectively modify the tumor microenvironment for improved efficiency of cancer therapy. The theoretical predictions show a good agreement with relevant experimental observations. This study aimed to deepen our understanding of tumor ECM may be conducive to novel anticancer strategies.

Nonequilibrium Thermodynamics and Scale Invariance

A variant of continuous nonequilibrium thermodynamic theory based on the postulate of the scale invariance of the local relation between generalized fluxes and forces is proposed here. This single postulate replaces the assumptions on local equilibrium and on the known relation between thermodynamic fluxes and forces, which are widely used in classical nonequilibrium thermodynamics. It is shown here that such a modification not only makes it possible to deductively obtain the main results of classical linear nonequilibrium thermodynamics, but also provides evidence for a number of statements for a nonlinear case (the maximum entropy production principle, the macroscopic reversibility principle, and generalized reciprocity relations) that are under discussion in the literature.

Phenomenological study on heat and mass coupling mechanism of waxy crude oil pipeline transport process

ABSTRACTBased on the phase equilibrium model of the paraffin wax precipitation in the process of oil pipeline transportation, theory and method of non-equilibrium thermodynamics were applied to obtain the linear phenomenological equations for the cross-interaction of heat and mass transfer during pipeline transport, which were derived from the irreversible entropy production rate equation. Then, the analysis of the irreversible heat flow and the mass flow were carried out, and the mathematical expressions of the phenomenological coefficient of liquid phase, the phenomenological coefficient of solid phase flow, and the heat flow phenomenological coefficient were obtained. Taking a waxy crude oil transportation pipeline in Daqing Oilfield as an example, based on the analysis of liquid–solid phase equilibrium, the irreversible linear phenomenological mechanism of heat and mass coupling in waxy crude oil pipeline transportation was analyzed in detail from three levels: phenomenological coefficients which reflect characteristic of the effect of force on flow in heat and mass transfer; thermodynamic forces which trigger heat and mass transfer; transmitted heat and mass flow density, providing a theoretical basis for the further study of the wax deposition in the process of pipeline transportation.

Galilean relativistic fluid mechanics

Single component nonrelativistic dissipative fluids are treated independently of reference frames and flow-frames. First the basic fields and their balances, then the related thermodynamic relations and the entropy production are calculated and the linear constitutive relations are given. The usual basic fields of mass, momentum, energy and their current densities, the heat flux, pressure tensor and diffusion flux are the time- and spacelike components of the third order mass-momentum-energy density-flux four-tensor. The corresponding Galilean transformation rules of the physical quantities are derived. It is proved, that the non-equilibrium thermodynamic frame theory, including the thermostatic Gibbs relation and extensivity condition and also the entropy production is independent of the reference frame and also the flow-frame of the fluid. The continuity-Fourier-Navier-Stokes equations are obtained almost in the traditional form if the flow of the fluid is fixed to the temperature. This choice of the flow-frame is the thermo-flow. A simple consequence of the theory is that the relation between the total, kinetic and internal energies is a Galilean transformation rule.

Liquid-solid phase transition of physical hydrogels subject to an externally applied electro-chemo-mechanical coupled field with mobile ionic species.

In this study, a model was multiphysically developed for the simulation of the phase transition of physical hydrogels between liquid solution and solid gel states, subject to an electro-chemo-mechanically coupled field, with the effect of the mobile ionic species in the solution. The present model consists of the governing equations for the equilibrium of forces and the conservation of mass, Maxwell's equations, and an evolution equation for the interface. Based on the second law of thermodynamics, the constitutive equations are formulated from the energy viewpoint, including a novel formulation of free energy with the effect of crosslink density. The present model may be reduced to Suo's non-equilibrium thermodynamic theory if the interface is ignored when only a single phase exists. It may also be reduced to Dolbow's model for gel-gel phase transition when the electric field is ignored. Therefore, the present model becomes more generalized since it is able to represent both the bulk phase and the interface behaviors, and the mechanical field is simultaneously coupled with both the electric and chemical fields. In the first case study, the system at equilibrium state was numerically investigated for analysis of the influences of the electrical and chemical potentials as well as the mechanical pressure externally imposed on the boundary of the system domain. The second case study presents a spherically symmetrical solution-gel phase transition at non-equilibrium states, with the emphasis on the evolution of both the interface and electrochemical potentials.

Interface behavior of physical hydrogel subject to solution-gel phase transition and nonlinear deformation

In this paper, a multiphysics model is developed for simulation of the interface behavior of physical hydrogel subject to solution-gel phase transition and nonlinear deformation, in which the solution and gel states are considered as two distinct phases and separated by a sharp interface approach. The presently developed model accounts for the multiphysics effects of the mechanical, chemical and thermal coupled fields. Apart from the classical governing equations for mass and energy conservations, and for the force equilibrium in the two bulk phases and on their interface, an additional equilibrium equation for a so-called configurational force is imposed in the two bulk phases and on their interface for the effect of the solution-gel phase transition. The corresponding configurational heating and mass supply are also proposed to account for energy change due to the migration of the control volume. By the second law of thermodynamics, the constitutive equations are formulated, including an evolution equation for the interface. The present model will reduce to Suo's non-equilibrium thermodynamic theory, if the interface is ignored when only a single bulk phase exists, i.e. no phase transition occurs. In order to model the phase behavior of physical hydrogel, which directly results from breaking and forming of crosslinks, a novel formulation of the free energy is proposed, which accounts for the effect of crosslink density to characterize the phases, and may reduce to that for a chemical hydrogel when the crosslink density is constant. Moreover, the present model may also reduce to Ji's work that coupled the mechanical field with the thermal field if the chemical field is ignored, or to Dolbow's chemo-mechanical model when the thermal field is ignored. Therefore, the present model is more generalized since the mechanical field is coupled with both the thermal and chemical fields simultaneously, and thus is able to model both the bulk phase and the interface behaviors. As case studies, the system at equilibrium state and a spherically symmetrical solution-gel phase transition at non-equilibrium states are investigated numerically for analysis of the effects of mobility, surface tension and other parameters on the interface behavior.

A fully coupled THM model based on a non-equilibrium thermodynamic approach and its application

Summary In this study, a fully coupled thermo-hydro-mechanical (THM) theoretical model, called the TSINGHUA-THERMOSOIL model, which is applicable in saturated soils, was developed based on a non-equilibrium thermodynamic approach (see Groot S, Mazur P. Non-Equilibrium thermodynamics. Amsterdam: North-Holland Pub. Co., 1962). This model simplifies the mathematical description of a THM coupling system to the modeling of a group of migration coefficients and energy functions by means of the non-equilibrium thermodynamic theory. The important concept of granular entropy was introduced for describing the granular fluctuation and the resulting transient elasticity. Therefore, non-elastic mechanical constitutive relations that do not require such concepts as yield surface and flow rule are obtained. The physical process of bound pore water transforming into free water when the temperature rises was taken into consideration for describing the phenomenon of the volumetric compression of normally consolidated and slightly over-consolidated clays under non-isothermal conditions. The behavior of thermal consolidation and drained shear tests at different temperatures for saturated Kaolin clay with different over-consolidation ratios (OCR) were simulated using this model. The effect of the OCR value, the heating rate and temperature cycling on the thermal consolidation and the effect of the temperature on the shear strength were analyzed and compared with existing experimental data. The results showed that the model proposed in this paper can accurately describe the thermal consolidation and the basic law of shearing for saturated soil, which preliminarily proves the validity of the model. Copyright © 2016 John Wiley & Sons, Ltd.

A theoretical model for the porosity–permeability relationship

An analytical permeability model is proposed for incompressible flow in porous media. Based on a general non-equilibrium thermodynamic stability theory, the model is derived from maximizing the entropy production rate to achieve a stable system. The resulting formula is in a form similar to previous empirical equations, but with calculable coefficients. Both three-dimensional lid-driven cavity and cubicle natural convection problems have been computed, via a modern computational fluid dynamics (CFD) solver, for numerical investigations of its performance.

Non-equilibrium thermodynamics and stochasticity: a phenomenological look on Jarzynski’s equality

The theory of phenomenological Non-equilibrium Thermodynamics is extended by includimg stochastic processes in order to account for recently derived thermodynamical relations such as the Jarzynski equality. Four phenomenological axioms are postulated resulting in a phenomenological interpretation of Jarzynski's equality. Especially, considering the class of Jarzynski processes Jarzynski's equality follows from the axiom that the statistical average of the exponential work is protocol independent.

Exergy transfer characteristics of gas-solid heat transfer through sinter bed layer in vertical tank

The examination of exergy transfer characteristics caused by gas-solid heat transfer through sinter bed layer in vertical tank has been presented. Correlations involving relevant variables to predict the mean exergy transfer coefficient, the mean exergy transfer Nusselt number and the non-dimensional exergy flux have been derived by applying the second law of thermodynamics and non-equilibrium thermodynamics theory. The relationships of mean exergy transfer Nusselt number with the heat transfer Nusselt number, Reynolds number, the non-dimensional heat flux and the non-dimensional pressure drop are determined. The experimental results of exergy transfer characteristics in sinter bed layer with different gas superficial velocity, sinter particle diameter and bed layer height are obtained from homemade gas-solid heat transfer setup, and the effects of air outlet temperature, non-dimensional temperature and Reynolds number on the exergy transfer characteristics are analyzed. The research results show that for a given experimental condition, the mean exergy transfer Nusselt number gradually decreases with the increase of Reynolds number and sinter bed layer height. The mean exergy transfer Nusselt number would be less than zero for a lower air outlet temperature, which is pointless for gas-solid heat transfer process in sinter bed layer.